Interplanetary travel is not undertaken in a straight line. Instead, rockets follow a trajectory which loops past the moon or planets along the way to get a slingshot boost through the gravitational field of the object.
However, assuming you travelled in a straight line from the Earth to Neptune and the journey were planned so that the orbits of the Earth at launch and that of Neptune at arrival were in a straight line (Earth's aphelion and Neptune's perihelion), it would take approx 3.9 years.
It took twelve years to get from earth to neptune.
it take Triton about 6 days to orbit Neptune
60,190 days164.79 years89,666 Neptune solar days
It takes Neptune 165 years to take a full rotatation around the sun.
32 days by car
288 years
about 164 years
it takes 16.1 days to rotate
16.11 hours.
16.11 hours.
12 hours
I am sorry to say but neptune orbits the sun not the moon.